
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:title>Properties of semi-elementary imsets as sums of elementary imsets</dc:title>
  <dc:subject>Markov basis</dc:subject>
  <dc:subject>semi-graphoid</dc:subject>
  <dc:subject>toric ideal</dc:subject>
  <dc:description>We study properties of semi-elementary imsets and elementary imsets introduced by Studeny [10]. The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.</dc:description>
  <dc:contributor>Kashimura, Takuya</dc:contributor>
  <dc:contributor>Sei, Tomonari</dc:contributor>
  <dc:contributor>Takemura, Akimichi</dc:contributor>
  <dc:contributor>Tanaka, Kentaro</dc:contributor>
  <dc:date>2011</dc:date>
  <dc:date>2011</dc:date>
  <dc:type>Article</dc:type>
  <dc:format></dc:format>
  <dc:format>application/pdf</dc:format>
  <dc:identifier>islandora:1007829</dc:identifier>
  <dc:identifier>http://hdl.handle.net/10560/islandora:1007829</dc:identifier>
  <dc:source>MATH / Applied Mathematics</dc:source>
  <dc:source>Illinois Institute of Technology</dc:source>
  <dc:source>Journal of Algebraic Statistics</dc:source>
  <dc:language>en</dc:language>
  <dc:rights>Open Access</dc:rights>
</oai_dc:dc>